Integrated optical chips with optical functions typically use low index difference waveguides, and these optical chips generally contain up to only two or three optical functions. FIG. 1 shows a typical planar dielectric waveguide, which is an example of a two-dimensional waveguide. Low index difference waveguides, such as those used in optical chips and for the optical fiber waveguides for input to and output from optical chips, are three-dimensional versions of such planar dielectric waveguides. These low index difference waveguides 10 include a core material 12 surrounded by a cladding material 14. The core material 12 can have an arbitrary cross-section, including a circular, elliptical, square, or rectangular cross-section embedded in the cladding material 14. The index of refraction n1 of the core material 12 is slightly larger than the index of refraction n2 of the cladding material 14. The index difference Δn for the index of refraction n1 of the core material 12 and the index of refraction n2 of the cladding material 14 (Δn=n1−n2) is therefore generally very small. A useful metric is delta (Δ), which is defined as Δn/ncladding for this type of waveguide, and is generally around 0.01 (1 percent) to 0.04 (4 percent), and certainly less than 0.1 (10 percent). In other words:
  Δ  =                              n          1                -                  n          2                            n        2              ⪡    1.  
A ray of light moving in the z direction in FIG. 1 (from left to right) is guided by total internal reflection within the core material 12 if the angle of incidence θ of the ray with respect to the interface between the core material 12 and the cladding material 14 is larger than a critical angle θc. This critical angle θc equals sin−1(n2/n1). For low index difference waveguides, due to the indices of refraction n1, n2, the angle of incidence θ must be large in order for total internal reflection to guide the light ray through the waveguide.
The typical optical chips having low index difference waveguides are generally large, wafer-sized chips. This large size results because the low index difference waveguides can adequately guide light only if bends in the waveguides have large radii. If small bending radii are used with these low index difference waveguides, large losses result because light is loosely confined within the core material 12. Low index difference waveguides therefore function adequately without large losses only with relatively high bending radii, and it is therefore difficult to perform optical functions in small areas using these low index difference waveguides.
The use of higher index difference waveguides reduces the minimum bending radii while maintaining adequate performance (that is, low loss), and therefore reduces the area required to perform the optical functions. The index of refraction n1 of the core material 12 is significantly larger than the index of refraction n2 of the cladding material 14 for such a higher index difference waveguide. Delta (Δ) for a high index difference waveguide is typically at least as large as 0.1, 0.2, or 0.3. In other words:
  Δ  =                              n          1                -                  n          2                            n        2              ≥          0.1      .      In such a high index difference waveguide, total internal reflection of light propagating through the waveguide is achieved for smaller angles of incidence θ for a ray of light, and the minimum bending radii for which performance is adequate is reduced.
The use of high index difference waveguides does have drawbacks. Because the fiber optic waveguides used for input to and output from optical chips are typically low index difference waveguides, a higher loss results in the coupling between the low index difference optical fiber waveguides and the high index difference waveguides on the optical chip. In addition, scattering loss increases for higher index difference waveguides, and therefore a larger loss in optical signals can result over a shorter length than for typical low index difference waveguides.